Problem: $ \left(\dfrac{4}{9}\right)^{-\frac{1}{2}}$
Solution: $= \left(\dfrac{9}{4}\right)^{\frac{1}{2}}$ Figure out what goes in the blank: $\Big(? \Big)^{2}=\dfrac{9}{4}$ Figure out what goes in the blank: $\Big({\dfrac{3}{2}}\Big)^{2}=\dfrac{9}{4}$ So $\left(\dfrac{4}{9}\right)^{-\frac{1}{2}}=\left(\dfrac{9}{4}\right)^{\frac{1}{2}}=\dfrac{3}{2}$